Particle System not utilizing UV mapped texture
You need to be emitting the particles from the Faces not the Vertices.
Think about it, you are trying to control the distribution of the particles with a texture, textures are mapped to the faces.

In the particle settings under the Emission section change the "Emit From:" value to Faces.


Now if you edit the UV map, you may need to refresh the particle system. You can do that by toggling it to emit from Verts then back to Faces.

That right there takes care of 95% of your problem.

(I changed the color of the spheres to be red just to show up better)  

To fix those last few stragglers, just bump the contrast of the texture up a bit. There are a few pesky gray values in the texture (probably from some island), that is what is making the icospheres appear in the ocean.

Make sure you are changing the particle's texture, not the material's texture.
Open up the Color section and increase the contrast (I found that 1.1 worked fine here.)